Jacques Herzog is one of the architects that almost everyone agrees is a genius. The Swiss superstar recently gave a lecture at London's Union Chapel, attended by the great and good of British architecture, at which he talked a rapt audience through some of the most innovative and beautiful building projects anywhere in the world. The comments of one architect at the end were final: "I think I might as well pack up and go home."

With his partner Pierre de Meuron, Herzog's record in Britain is excellent - two buildings, two hits. Their first work here was Tate Modern, which remains the most successful new arts institution in Europe, despite brickbats from British architects such as Will Alsop. Their second, the Laban dance centre in Deptford, London, designed in collaboration with artist Michael Craig-Martin, has been comprehensively lauded by critics and public alike. Last year, it won Herzog and De Meuron the Stirling prize, Britain's most prestigious building award. That wasn't the practice's only success last year: it also completed the new Prada store in Tokyo, one of the most talked-about buildings in the world. And on Christmas Eve, construction began on its biggest project yet: the Olympic Stadium, which will form the centrepiece of the Beijing Olympics in 2008.

The 100,000 capacity arena promises to be the most remarkable stadium since Gunter Behnisch's 1972 Olympic Stadium in Munich. It looks like a giant bird's nest, with a mass of structural members intertwined to form its huge basket. The roof of the building is organised in a circular pattern, and every element is structurally vital. There isn't a single perpendicular column in the building; instead, transparent panels sit between strands of the basket, set back from the structure and almost invisible from outside. Inside the stadium, the tiers of seating will have no visible underside, while the balconies will be voids carved from the mass of the structure itself. The plinth on which the building sits will be treated in a similar way, with the structure continuing downward as if taking root. "So far the building, from competition to now, has become better and more radical," says Herzog, with as close to a glint as you are likely to see from him.

Herzog is one of the brave architects willing to make buildings that are not only deliberately spectacular, but have aspirations to become a living part of the city. It's his intention that the Beijing stadium will be "the most visible icon of contemporary China". And he compares the space around the Beijing stadium to that around the Eiffel Tower in Paris: for him, the plaza created beneath the tower - a space of meeting and promenading - shows the potential to create unexpected public spaces.

"We want the space around the stadium to be something new - and to make something that has a permanent role in public life. In China, public space is real, unlike in Tokyo. The Chinese are more extrovert than the Japanese. We want the stadium to have an iconic role and become a public space." The same thinking has been applied to the practice's soon-to-be completed Forum Barcelona building in the Catalan capital: a huge, triangular blue building lifted off the floor to create a covered public plaza.

Herzog and de Meuron became famous in architectural circles on the back of severe buildings such as the glassy Goetz Gallery in Munich, Germany (completed in 1992, and which Herzog still describes as the practice's best building) and the Ricola Factory building in Switzerland (1991). With the Beijing stadium, Herzog's designs move away from the geometric rigour of the practice's early work, but he doesn't think we should be surprised. "Some people, especially in England, put us in this drawer of minimalism and the right angle," he says. "But if they didn't put us in the drawer they would see that there is a culture to what we do, and we are very radical in the way we present it. Radical rectangle, radical minimalism, radical something else. We try to push things to their boundaries."

The practice's work seems to be striving for a more universal appeal through forms that recall naturally occurring shapes. "It's to give a project a language that you can kind of unconsciously read and understand," says Herzog. "Nature has that. But I'm not a natural romantic at all, it's just that you can learn from that." He still considers his work to have a more "intellectual" approach than that of Frank Gehry, the architect of Bilbao Guggenheim Museum. When he talks about his buildings, Herzog stresses the process of making them, and uses metaphors of natural processes or impulses to communicate his ideas. Prada Tokyo, for example, was a commission that gave the practice the luxury of experimenting with different approaches, layouts and materials. Herzog describes how final design decisions, particularly on issues such as interior finishes, were made only after extensive practical testing. The coverings for the building's structure, for instance, went through stages of being clad in felt, rubber, stone, wood, resin, silicone and metal, all in the name of suppressing the rawness of the steel beams.

While this might sound indulgent, Herzog has the air of an architect who has seen it all. His persona exudes a certain distance - although that belies his creative focus. "You are very full of passion with something," he says. "But at the same time you keep a certain distance from what you produce everyday, with a view that is almost bored, so you can in a more reliable way say, 'Yes, that's what's interesting', or 'That's just another step in a too idiosyncratic dimension'."

He has a horror of explaining his work, and would rather leave interpretation to be thrust upon it: "The more you push your work in a certain direction, the more there's also a danger in doing things for the sake of themselves. It's so clear that architecture should have a certain ro bustness, a certain simplicity, a certain self-evidence. Even if it's the most daring thing, it must stand by itself."

Such is the practice's success that it now employs around 200 people, working on 50 projects in offices in Basel, London, San Francisco, Munich and Barcelona. And the profusion of radical forms coming out of the practice is due, in part, to an increasing confidence at dealing with large-scale buildings. "I understand more now that an important part of the success of a building is what I call 'attraction'," says Herzog. "You attract people, but you are also attractive; it's like a natural stimulus for people to go somewhere." Despite now having £100m building budgets to manage, there is little chance of Herzog playing safe in the near future. "We must find a way to do something forbidden," he says. "Without getting punished."

· A version of this article appears in this month's edition of Icon magazine.